Does this emulate the games loaded onto it or does it play gb, gbc, gba games natively on gba? and are the nes roms emulated because i'm assuming yes. Also if you use this on a DS/DSlite would the gb and gbc games be emulated or run native? sorry if dumb questions i just cant find any info when googling it.
If you peer into the cart slot of your GBA/GBA SP there will be a little black slider thing one side. When this is pushed in then it physically transforms the GBA/GBA SP into a GBC. Such modes can't be accessed by software or anything from GBA mode.
To this end if you put an original GB/GBC game cart in your GBA it will transform itself into a GBC and play accordingly. GBA flash carts can't do this, save for one very rare and very old flash cart if you have a special adapter (called the GB Bridge), but the GBA mode is just powerful enough to emulate the gameboy and gameboy color as well (some homebrew coders were not even sure that was going to happen at one point).
Every GBA flash cart however operates natively, which is to say it appears to the GBA* as a normal cart as far as it is concerned. Some are better than others at some things, though for most practical purposes if it is not a GBA slot supercard or one of the clones of it (both of which have slower memory and thus slowdowns, crashes, patches and incompatibility) then if it fits in the memory it will run.
The Omega also provides you a bunch of emulators in its loader thing for a bunch of systems. To state the obvious everything that is not GBA will be emulated. Emulating a system on itself is a more or less nonsensical phrase, ignoring virtualisation on a PC then for some older devices then the carts themselves might have provided extra chips to do stuff with (which the flash cart will then have to emulate or simulate) but the GBA did not have anything like that really. There was the occasional extra sensor or something but most of those have long been sorted --
http://gbatemp.net/threads/buying-a-gba-flash-cart-in-2013.341203/page-18#post-4756995
*to be a complete pedant I do have to note there are a few "adapters" (stuff like the things that allow you to play GBA games on a SNES) that are actually GBA ROM dumpers coupled with an emulator. Owing to the way all but two GBA games (
https://mgba.io/2015/10/20/dumping-the-undumped/ ) work this works fine for commercial carts but all but a handful of old flash carts if set up in a specific way act differently and thus won't work with those devices. However those devices aren't good so easy enough to dodge those.